Touil et al. [1]} examined an alternative
Holevo quantity with the measurement on the fragment side,
\(\chi \left(\mathcal {S}:\check{\mathcal {F}}\right)=\max _{\Pi _{\mathcal {F}}}\chi \left(\mathcal {S}:\Pi _{\mathcal {F}}\right)=\max _{\Pi _{\mathcal {F}}}\left[H_{\mathcal {S}}-\sum _{f}p_{f}H_{\left.\mathcal {S}\right|f}\right],\) 
